Digital implementation of a tracking filter

ABSTRACT

Methods and systems for tracking an electronic signal corresponding to an operating frequency of an electronic component are provided. A method may include sampling the signal to determine previous and current time samples of the signal. A frequency of interest in the signal may also be pre-warped to decrease adverse warping effects resulting from processing signals having relatively higher operating frequencies. The previous and current time samples of the signals, along with the pre-warped frequency of interest, may be input into a digital tracking filter. The digital tracking filter may be configured to execute one or more algorithms on the previous and current time samples and the pre-warped frequency of interest to estimate a current operating frequency.

BACKGROUND

The invention relates generally to signal processing, and morespecifically, to filtering techniques for electronic signals.

Various electronic systems including electric drives or motors mayoperate by converting electric energy into mechanical energy. Anelectronic system may operate at one or more operating frequencies, orcycles of a mechanical motion per second. The electronic system maytrack each operating frequency to determine a condition of the system.Changes in an operating frequency, or deviations from an appropriaterange of an operating frequency, may indicate that a drive in the systemis not operating normally. For example, mechanical parts may besubjected to general wear and tear during their lifetime. Further, partsof an electronic system may be subjected to abnormal conditions whichaffect the operation of the system. As a result, the components of theelectronic system may eventually fail, which may lead to faults and/orinefficient operation of the electronic system.

Some electronic systems may be configured to detect changes in theoperating frequencies in the system. Detection of such changes inoperation may alert an operator of the system that a part may needrepair or attention, or that the system is not operating efficiently.For example, the electronic system may determine that a particular drivein the system is operating at less than an appropriate operatingfrequency, and may be in need of repair or replacement.

Generally, filters may be used to determine and/or separate certainfrequency bands in a signal, and may be used to detect conditions in anelectronic system by determining one or more operating frequencies inthe system. In some electronic systems, the frequency components mayvary within a relatively wide range, and static filtering techniques maybe inefficient in detecting whether a varying operating frequencyremains in an acceptable range. For example, electric drives such asmotors or generators may have constantly changing rotational speeds, anda static filter may not be configured to identify when the operatingfrequency is in a normal or abnormal range. Thus, electronic systems maybenefit from a filtering method adapted to distinguish and/or track oneor more operating frequencies dynamically.

BRIEF DESCRIPTION

One embodiment relates to a method for tracking a parameter of interestwithin a frequency of interest. The method includes periodicallysampling the values of the parameter of interest to obtain a sampledvalue for a current time step, as well as a sampled value for a previoustime step. Obtaining the sampled values and the combination of sampledvalues may be based on a known current operating frequency and a knowntime step duration, and may determine the parameter of interest.

Another embodiment includes a method for tracking an operating frequencyof an input signal. The method may be largely performed by a processorin an electronic system, and may include receiving an input signalcorresponding to an operation of a device in the system. The method maythen include pre-warping a frequency in the input signal and digitizingthe input signal to determine a previous time sample and a current timesample of the digitized input signal. The method may then includeexecuting one or more algorithms using the pre-warped frequency ofinterest, the previous time sample, and the current time sample tooutput an estimate of the signal at the operating frequency.

In another implementation, an electronic system is provided. Theelectronic system includes a processor configured to provide anelectronic signal corresponding to an operation of a component in thesystem. For example, the signal may be an analog signal generated inresponse to motion of the component. The processor may also beconfigured to sample the signal to obtain a previous time sample and acurrent time sample of the reference, and also to pre-warp a frequencyof interest in the signal. The frequency of interest may be based on aknown operating frequency of the component. The processor may further beconfigured to estimate the signal at the operating frequency based onthe pre-warped frequency of interest, the previous time sample, and thecurrent time sample.

DRAWINGS

These and other features, aspects, and advantages of the presentinvention will become better understood when the following detaileddescription is read with reference to the accompanying drawings in whichlike characters represent like parts throughout the drawings, wherein:

FIG. 1 is a block diagram illustrating an overview of a digital trackingfilter, in accordance with one embodiment of the present techniques;

FIG. 2 is a block diagram representing how a signal may be input into atracking filter of FIG. 1;

FIG. 3 is a block diagram representing a pre-warping function in thetracking filter of FIG. 1;

FIG. 4 is a diagram representing a tracking filter function; and

FIGS. 5A and 5B are graphs depicting the digital tracking of anelectronic signal, where estimates are made without pre-warping, andwith pre-warping.

DETAILED DESCRIPTION

Electronic systems may often be configured to monitor one or moreoperating frequencies of components (e.g., drives, motors, etc.) in thesystem. Monitoring the operating frequencies of system components mayenable the detection of a component not operating at an appropriatefrequency, which may indicate that the component is in need of attentionand/or the system is not operating efficiently. The components of anelectronic system may typically operate at varying frequencies, and suchoperating frequencies may not be known in advance. To track and/ormonitor a signal at the frequency of interest when the frequency mayvary and/or may be unknown, filtering methods may be adapted todetermine the value of a frequency dynamically (e.g., track the value ofan operating frequency in a signal even when the operating frequency isconstantly changing). The present techniques include methods ofdigitally tracking electronic signals given a reference frequency inputin an electronic system. A frequency component in an electronic systemmay be determined even when the system is operating at relatively highfrequencies. Furthermore, while the filtering of motor drives may beused as one example of an application for the present techniques,embodiments of the present techniques may apply for any electronicsignal.

Turning now to the figures, FIG. 1 illustrates an overview of a process10 for tracking the operating frequency of an electronic systemcomponent. Components and/or circuitry involved in the process 10 ofFIG. 1 include an input integrator circuit 18, a frequency pre-warpingcircuit 20, and a tracking filter 30, which are illustrated in furtherdetail in FIGS. 2-4, respectively. Beginning first with FIG. 1, theprocess 10 depicts one embodiment of a technique for tracking theoperating frequency of a component in an electronic system. The signalu(t) 12 may be any signal having the desired frequency component. Thefrequency component may be set by the frequency input w(t) 14, which maybe a signal having the frequency to be tracked in the signal u(t) 12. Inone embodiment, the signal w(t) 14 may be may represent a rate at whichan electric system component is operating (e.g., based on cycles ofmotion), and the process 10 may be configured to track a frequencycomponent of the signal u(t) 12 based on the frequency input w(t) 14.

In one embodiment, the signal 12 and the frequency input signal 14 maybe analog signals corresponding to a continuous operation of theelectric system component. The signal 12 may be sent through circuit 18configured to output amplified, discretized, and time delayed signals ofthe signal 12.

Certain electrical systems may include components with high operatingfrequencies. When processing a high frequency signal, frequency warpingmay occur, which may result in aliasing or distortion of an input signaland reduce the ability to properly track a frequency component in thesignal. To accommodate for frequency warping when input signals 12and/or 14 have high frequencies, the process 10 may also include afrequency pre-warping circuit 20 configured to pre-warp the inputfrequency signal 14. Thus, a pre-warped input signal 22 may betransmitted to a tracking filter 30, such that the negative effects ofwarping (e.g., aliasing, distortion) which occurs in the filtering of ahigh-frequency signal may be decreased, and the tracking filter 30 maymore accurately determine the value of the center frequency component ofthe input signal. The input integrator circuit 18 may also output a timedelayed signal 24 into the tracking filter 30. As will be laterdiscussed, the tracking filter 30 may make a digitized estimation of thefrequency component in the signal u(t) 12 as an output 32 to theelectronic system.

Furthermore, the input integrator circuit 18 may also output adiscretized signal 28. The discretized signal 28 may be a sampled valueof the signal u(t) 12, which is represented as a continuous signal 26from the input integrator circuit 18. The digitized estimation output 32from the tracking filter 30, the continuous signal 26, and/or thediscretized signal 28 may be provided to other components in anelectronic system, such as to a processor, which may analyze each signalor compare the signals to determine a condition of the operatingfrequency. For example, the digitized estimate output 32 from thetracking filter 30 may enable an electrical system (e.g., the processor)to track changes in the signal of the component being monitored. Asdiscussed, the operating frequency of an electrical system component,such as a motor or a drive, may vary throughout the operation of thesystem. By monitoring or analyzing the signal component at the output32, the system 38 may determine a certain condition about the componentbeing tracked.

The input integrator circuit 18 of the process 10 (from FIG. 1) isdepicted in FIG. 2. The input frequency signal 14 may be transmitted toan integrator 40 which integrates the signal 14 over time. The integral42 may be amplified by multiplexing (e.g., via a multiplexer 46) with aconstant value 44 to circuitry 48 configured to change the amplitude ofthe integrated input 42. A function used to modify the amplitude of theinput 42 may be any signal. One example of a function which enables theamplitude of the input 42 to be changed by varying the constant 44 maybe represented as f(u)=sin(u(1))*u(2), where u(1) represents theintegral 42 of the input signal 14, and where u(2) represents thevariable constant 44. In some embodiments, the variable constant 44 maybe changed depending on the application, or depending on thecharacteristics of the frequency to be tracked. Thus, one output 26 fromthe circuitry 48 may be an amplified input signal 26.

The amplified input signal 26, which may be from any source in additionto that described, may also be directed to a zero order hold 50, whichdiscretizes (e.g., samples) the continuous amplified input signal 26 tooutput a discrete signal 28. The discrete sample 28 may also betransmitted to a unit delay circuit 52. In one embodiment, the unitdelay circuit 52 may include one or more delay units configured toreceive the current sample of the input signal 28 and generate a delaytime by one sample time T to output a previous sample in time 54. Theunit delay may be represented by u(K−1)T, where the K−1 represents aprevious sample number of the current sample number K. The previoussample 54 may be added with the current sample 28, represented as u(KT)in the adder 56 to output a signal 24 having the previous and thecurrent sample. This time delayed input signal 24, having the previousand current samples, may be represented by u(KT)+u(K−1)T. Thus, in oneembodiment, the input integrator circuit 18 may output a continuoussignal 26 which may be amplified according to a variable constant 44.The input integrator circuit 18 may also output a discrete, sampledinput signal 28, as well as a time delayed input signal 24. As will belater discussed, the time delayed input signal 24 may be used in thetracking filter 30 to track the signal at the operating frequency of anelectronic system component based on current and previous frequencyvalues. The continuous and amplified input signal 26 and the discreteinput signal 28, including the current sample, may be output by theinput integrator circuit 18 such that the electronic system 38 (e.g., aprocessor in the system 38) may use the signals for further analysesand/or processing to evaluate an estimate of the operating frequency ofthe electronic system component.

As discussed, electronic systems may often include components whichoperate at high frequencies. Signal processing of high frequency signalsmay sometimes result in frequency warping of the signal. Thus, whenfiltering a digitized signal, warping may result in aliasing and/ordistortion, which may affect the accuracy of estimating the value of thecenter frequency component (e.g., an operating frequency) of the inputsignal. One method of preventing the negative effects of signal warpingmay be to compensate for possible warping by first pre-warping an inputsignal before processing the input signal. A continuous time circuitdesign may be configured to pre-warp a signal to compensate forfrequency warping, and may be represented by the equation below:

$\begin{matrix}{\omega_{a} = {\frac{2}{T_{s}}{\tan \left( {\omega \frac{T_{s}}{2}} \right)}}} & {{eq}.\mspace{14mu} (1)}\end{matrix}$

In eq. (1), the continuous time filter frequency ω_(a) corresponds tothe discrete time filter frequency ω. In one embodiment, the inputfrequency signal 14 (as in FIG. 1) may be pre-warped by the frequencypre-warping circuit 20 in FIG. 3, which may correspond to the operationdescribed by eq. (1). The frequency of the input frequency signal 14ω₀(t) may first be multiplied by T_(s)/2, or half the sampling period,such that the tan(ωT_(s)/2) may be taken in block 60. An input of2/T_(s) 62 may be multiplied in block 64 by tan(ωT_(s)/2) to produce thepre-warped frequency 66. The pre-warped frequency may then bediscretized by the zero order hold 68. In some embodiments, thepre-warped frequency may already be discrete. The discrete pre-warpedfrequency 70 may be sent to a multiplexer 76, along with a previoussample of the discrete pre-warped frequency 74, which may have beendelayed by the unit delay circuit 72. The multiplexer 76 may output thecurrent and the previous pre-warped frequencies 22 in digital form.

The pre-warping circuitry 20 may thus output pre-warped signals 22 tothe tracking filter 30. In one embodiment, the tracking filter 30 maydigitally extract the frequency component corresponding to the frequencyof the input frequency signal 14, such that the extracted (e.g.,tracked) frequency component may be mapped into a discrete time system.The input frequency signal 14 may also be pre-warped to compensate forfrequency warping which may occur in filtering of high frequencysignals.

The pre-warped frequency signals 22 may be input into the trackingfilter 30, as generally depicted in FIG. 1 and further detailed in FIG.4. Also input into the digital tracking filter 30 is the time delayedinput signal 24, having both the previous and current samples of thediscrete input signal 28, which is output from the input integratorcircuit 18. The tracking filter 30 may involve algorithms whichband-pass filter the digitized input 24 to filter at a center frequencyof interest, and/or within a bandwidth a. The frequencies passed by thetracking filter 30 may be a range which encompasses the operatingfrequency of the electronic system component that is being monitored inthe process 10 (as in FIG. 1). The bandwidth a may be selected duringthe design of the tracking filter 30, or alternatively, the bandwidth amay be selected during the operation of the system 38, and may bealtered depending on the applications of the system 38 or thefrequencies to be tracked. For example, the bandwidth a may be selectedto be two times the expected operating frequency of the electronicsystem component monitored in the process 10, or three times theexpected operating frequency for detecting conditions such as groundfaults.

In one embodiment, the tracking filter 30 may be configured to executealgorithms based on the equation below:

$\begin{matrix}{\begin{bmatrix}{x_{1}({KT})} \\{x_{2}({KT})}\end{bmatrix} = {{A\begin{bmatrix}{{x_{1}\left( {K - 1} \right)}T} \\{{x_{2}\left( {K - 1} \right)}T}\end{bmatrix}} + {B\left\lbrack {{u({KT})} + {{u\left( {K - 1} \right)}T}} \right\rbrack}}} & {{eq}.\mspace{14mu} (2)}\end{matrix}$

where K represents a current frequency sample, T represents the samplingtime, x₁(KT) represents the current estimate of the operating frequency32, and x₁(K−1)T represents a previous estimate of the operatingfrequency. The previous estimate may be used to determine a currentestimate 32. Matrix A may be a 2×2 matrix, and matrix B may be a 2×1matrix, both defined below:

$\begin{matrix}{A = {{\frac{1}{1 + {\frac{T}{2}a} + \left( {\frac{T}{2}{\omega_{0}({KT})}} \right)^{2}}\begin{bmatrix}1 & {{- \frac{T}{2}}{\omega_{0}({KT})}} \\{\frac{T}{2}{\omega_{0}({KT})}} & {1 + {\frac{T}{2}a}}\end{bmatrix}}{\quad\begin{bmatrix}{1 - {\frac{T}{2}a}} & {{- \frac{T}{2}}{\omega_{0}\left( {K - 1} \right)}T} \\{\frac{T}{2}{\omega_{0}\left( {K - 1} \right)}T} & 1\end{bmatrix}}}} & {{eq}.\mspace{14mu} (3)} \\{\mspace{79mu} {B = {\frac{1}{1 + \frac{2}{aT} + {\frac{T}{2a}\left( {\omega_{0}({KT})} \right)^{2}}}\begin{bmatrix}1 \\{\frac{T}{2}{\omega_{0}({KT})}}\end{bmatrix}}}} & {{eq}.\mspace{14mu} (4)}\end{matrix}$

The pre-warped input signal 22 may provide the input functions 78, 80,82, 84, 86, and 88, which include both a current and a previous timesample of the input signal. More specifically, each of the functions 78,80, 82, and 84 may represent a value in matrix A, and each of thefunctions 86 and 88 may represent a value in matrix B. Further,u(KT)+u(K−1)T from eq. (2) may be obtained by the time delayed inputsignal 24 output from the input integrator circuit 18.

The multiplication of matrix A by previous time sample estimates 121 and123 may be performed in blocks 90, 92, 94, and 96 where the previousestimates 121 and 123 are output by the unit delay circuits 120 and 122.The unit delay circuits 120 and 122 may be used for cross coupling, suchthat the time delayed estimates 121 and 123 of the outputs x₁(KT) 32 andx₂(KT) 118 may be sent back to blocks 90, 92, 94, or 96 to complete thematrix multiplication between matrix A and the previous time estimatesand matrix B with the input signal 24.

To obtain the output x₁(KT) 32, the tracking filter 30 may add theproducts 102 104, and 106. Product 102 may be a product (from block 90)of function 78, the a₁₁ position of matrix A, and the time sampleestimate 124. Product 104 may be a product (from block 92) of function80, the a₁₂ position of matrix A, and the time sample estimate 126.Product 106 may be a product (from block 98) of function 86, the b₁position of matrix B, and the input 24, u(KT)+u(K−1)T. The products 102,104, and 106 may be summed in block 114 to produce the output x₁(KT) 32.

To obtain the output x₂(KT) 118, the tracking filter 30 may add theproducts 108 110, and 112. Product 108 may be a product (from block 94)of function 82, the a₂₁ position of matrix A, and the time sampleestimate 124. Product 110 may be a product (from block 96) of function84, the a₂₂ position of matrix A, and the time sample estimate 126.Product 112 may be a product (from block 100) of function 88, the b₂position of matrix B, and the input 24, u(KT)+u(K−1)T. The products 108110, and 112 may be summed in block 116 to produce the output x₂(KT)118. The output x₁(KT) 32 may be an estimate of a current operatingfrequency of a component that is being monitored by the electronicsystem 38 via the process 10.

As discussed, the bandwidth value a may be selected at various stages,including during the hardware design of the filter 30, or anytime duringthe operation of the electronic system 38 comprising the filter 30.Furthermore, an electronic system 38 may have several filters 30 eachrunning in parallel, or a system 38 may have one or more filters 30which perform sequential frequency tracking at different bandwidthvalues. For example, a tracking filter 30 may operate for some amount oftime using one bandwidth a₁, and then operate for another amount of timeusing a second bandwidth a₂. The angular frequency ω₀ may also beselected based on the electronic system 38 and/or based on theapplication or the operating frequency of the system component that isbeing monitored by the process 10.

One example of a result of the tracking filter 30 in the process 10 maybe depicted in the graph 124 of FIGS. 5A and 5B. The graph 124 of FIG.5A, which displays amplitude (e.g., current, voltage, etc.) 128 overtime 126, plots an input signal 130 for a tracking filter, a digitalestimate of a tracking filter without pre-warping the signal, shown asline 132, and a digital estimate of a tracking filter with pre-warping,shown as line 134. The input signal 130 may correspond to an operatingfrequency of a component in an electronic system 38. In the graph 124,during the time before 2 seconds, the frequency is set to 60 Hz. At thisrelatively low frequency, pre-warping may not produce a substantiallydifferent estimate from not pre-warping, as each of the input signal130, the filtered estimate without pre-warping 132, and the filteredestimate with pre-warping 134 may be substantially similar. However, inhigh frequencies, pre-warping an input signal may result in a moreaccurate digital estimate. For example, after 2 seconds, the frequencyis set to 600 Hz. At this relatively high frequency, the estimate withpre-warping 134 may be substantially more accurate (e.g., closer to theinput signal 130) than the estimate without pre-warping 132.Furthermore, as depicted in the graph 136 of FIG. 5B, a tracking filterestimate without pre-warping 132 may degrade in accuracy over time,while the tracking filter estimate with pre-warping 134 remainssubstantially similar to the input signal 130.

Furthermore, in some embodiments, varying the bandwidth a or thesampling time T of the tracking filter 30 may result in high resolutiontracking, which may improve the accuracy of the digital estimate 132. Asseen in the graph 124, the digital estimate 132 follows the waveform ofthe input signal 130, such that signal peaks may be estimated, resultingin a substantially dynamic tracking of the frequency of the input signal130.

Thus, the present techniques may result in the substantially dynamictracking of any signal to estimate the operating frequency of acomponent in an electronic system. As discussed, monitoring theoperating frequency of a component, such as a motor or a drive, mayenable the electronic system to determine conditions in the system basedon changes or deviations in the operating frequency, including where orwhen a failure in the system has occurred.

While only certain features of the invention have been illustrated anddescribed herein, many modifications and changes will occur to thoseskilled in the art. It is, therefore, to be understood that the appendedclaims are intended to cover all such modifications and changes as fallwithin the true spirit of the invention.

1.-10. (canceled)
 11. A method for tracking an operating frequency of aninput signal, comprising a processor performing: receiving an inputsignal; pre-warping a frequency of interest of the input signal;digitizing the input signal; determining a previous time sample and acurrent time sample of the digitized input signal; and executing one ormore algorithms using the pre-warped frequency of interest, the previoustime sample, and the current time sample to output an estimate of theoperating frequency of the input signal.
 12. The method of claim 11,wherein the input signal comprises a sinusoidal waveform based on anoperation of an electronic system.
 13. The method of claim 11, whereinthe method operates during operation of an electronic system thatgenerates the input signal.
 14. The method of claim 11, wherein theoperating frequency is sufficiently high that executing the one or morealgorithms on the input signal would warp the operating frequency if theinput signal was not pre-warped.
 15. The method of claim 11, whereinexecuting one or more algorithms comprises using the pre-warped inputsignal, the previous time sample, and the current time sample in atracking filter to obtain the estimate.
 16. The method of claim 15,wherein executing one or more algorithms comprises determining aprevious value of the estimate and using the previous value of theestimate, the pre-warped input signal, the previous time sample, and thecurrent time sample in the tracking filter to obtain a current value ofthe estimate.
 17. An electronic system comprising a processor configuredto: provide a signal corresponding to an operating frequency of acomponent in the electronic system; sample the signal to obtain aprevious time sample of the signal and a current time sample of thesignal; pre-warp a frequency of interest in the signal; and estimate theoperating frequency based on the pre-warped frequency of interest, theprevious time sample, and the current time sample.
 18. The electronicsystem of claim 17, wherein the processor is configured to pre-warp thefrequency of interest to compensate for warping of the frequency ofinterest when the frequency of interest is relatively high.
 19. Theelectronic system of claim 17, wherein the processor is configured toestimate the operating frequency using algorithms based on therelationship: $\begin{bmatrix}{x_{1}({KT})} \\{x_{2}({KT})}\end{bmatrix} = {{A\begin{bmatrix}{{x_{1}\left( {K - 1} \right)}T} \\{{x_{2}\left( {K - 1} \right)}T}\end{bmatrix}} + {B\left\lbrack {{u({KT})} + {{u\left( {K - 1} \right)}T}} \right\rbrack}}$wherein K represents a current sample, T represents a sampling time,x₁(KT) represents a current estimate of the value of the parameter,x₁(K−1)T represents a previous estimate of the value of the parameter,u(KT)+u(K−1)T represents a current time sample of the parameter ofinterest in the frequency of interest added to a previous time sample ofthe parameter of interest in the frequency of interest, A represents$A = {{\frac{1}{1 + {\frac{T}{2}a} + \left( {\frac{T}{2}{\omega_{0}({KT})}} \right)^{2}}\begin{bmatrix}1 & {{- \frac{T}{2}}{\omega_{0}({KT})}} \\{\frac{T}{2}{\omega_{0}({KT})}} & {1 + {\frac{T}{2}a}}\end{bmatrix}}{\quad{{\begin{bmatrix}{1 - {\frac{T}{2}a}} & {{- \frac{T}{2}}{\omega_{0}\left( {K - 1} \right)}T} \\{\frac{T}{2}{\omega_{0}\left( {K - 1} \right)}T} & 1\end{bmatrix}\mspace{20mu} {and}\mspace{14mu} B\mspace{14mu} {represents}\mspace{20mu} B} = {{\frac{1}{1 + \frac{2}{aT} + {\frac{T}{2a}\left( {\omega_{0}({KT})} \right)^{2}}}\begin{bmatrix}1 \\{\frac{T}{2}{\omega_{0}({KT})}}\end{bmatrix}}.}}}}$
 20. The electronic system of claim 17, wherein theprocessor is configured to estimate the operating frequency based on thepre-warped frequency of interest, the previous time sample, the currenttime sample, and a previous estimate of the operating frequency.
 21. Amethod for tracking an operating frequency of an input signal,comprising a processor performing: receiving an input signal;pre-warping a frequency of interest of the input signal; digitizing theinput signal; determining a previous time sample and a current timesample of the digitized input signal; and determining an estimate of theoperating frequency of the input signal via a tracking filter.
 22. Themethod of claim 21, wherein the estimate of the operating frequency isdetermined by determining a previous value of the estimate and using theprevious value of the estimate, the pre-warped input signal, theprevious time sample, and the current time sample in the tracking filterto obtain a current value of the estimate.
 23. The method of claim 21,comprising pre-warping the frequency of interest to compensate forwarping of the frequency of interest when the frequency of interest isrelatively high.
 24. The method of claim 21, comprising estimating theoperating frequency using algorithms based on the relationship:$\begin{bmatrix}{x_{1}({KT})} \\{x_{2}({KT})}\end{bmatrix} = {{A\begin{bmatrix}{{x_{1}\left( {K - 1} \right)}T} \\{{x_{2}\left( {K - 1} \right)}T}\end{bmatrix}} + {B\left\lbrack {{u({KT})} + {{u\left( {K - 1} \right)}T}} \right\rbrack}}$wherein K represents a current sample, T represents a sampling time,x₁(KT) represents a current estimate of the value of the parameter,x₁(K−1)T represents a previous estimate of the value of the parameter,u(KT)+u(K−1)T represents a current time sample of the parameter ofinterest in the frequency of interest added to a previous time sample ofthe parameter of interest in the frequency of interest, A represents$A = {{\frac{1}{1 + {\frac{T}{2}a} + \left( {\frac{T}{2}{\omega_{0}({KT})}} \right)^{2}}\begin{bmatrix}1 & {{- \frac{T}{2}}{\omega_{0}({KT})}} \\{\frac{T}{2}{\omega_{0}({KT})}} & {1 + {\frac{T}{2}a}}\end{bmatrix}}{\quad{{\begin{bmatrix}{1 - {\frac{T}{2}a}} & {{- \frac{T}{2}}{\omega_{0}\left( {K - 1} \right)}T} \\{\frac{T}{2}{\omega_{0}\left( {K - 1} \right)}T} & 1\end{bmatrix}\mspace{20mu} {and}\mspace{14mu} B\mspace{14mu} {represents}\mspace{20mu} B} = {{\frac{1}{1 + \frac{2}{aT} + {\frac{T}{2a}\left( {\omega_{0}({KT})} \right)^{2}}}\begin{bmatrix}1 \\{\frac{T}{2}{\omega_{0}({KT})}}\end{bmatrix}}.}}}}$
 25. The method of claim 21, wherein the inputsignal comprises a sinusoidal waveform based on an operation of anelectronic system.
 26. The method of claim 21, wherein the methodoperates during operation of an electronic system that generates theinput signal.
 27. The method of claim 21, wherein the operatingfrequency is sufficiently high that executing the one or more algorithmson the input signal would warp the operating frequency if the inputsignal was not pre-warped.
 28. The method of claim 21, comprisingperiodically sampling the input signal via an input integrator.
 29. Themethod of claim 28, comprising combining sampled values of the inputsignal for a successive time steps via the integrator.
 30. The method ofclaim 28, wherein a sample time step is based upon a maximum anticipatedoperating frequency.